So it looks like I cannot implement a compareCustom which returns a NSComparisonResult? I feel like it should be possible.. but I am unable to figure out how. If someone can provide some advice I would really appreciate it!

According to the documentation custom sort doesn't work with SQLite persistent store:

The SQL store, on the other hand, compiles the predicate and sort
descriptors to SQL and evaluates the result in the database itself.
This is done primarily for performance, but it means that evaluation
happens in a non-Cocoa environment, and so sort descriptors (or
predicates) that rely on Cocoa cannot work. The supported sort
selectors are compare: and caseInsensitiveCompare:, localizedCompare:,
localizedCaseInsensitiveCompare:, and localizedStandardCompare: (the
latter is Finder-like sorting, and what most people should use most of
the time). In addition you cannot sort on transient properties using
the SQLite store.

So it seems you can't simply force NSFetchedResultsController to display sections in other than alphabetical order.

But you can use a workaround. Add additional, persistent attribute of integer type to your entity (let's call it sectionOrder). Set its value according to the states property (so it will be 0 for "Push", 1 for "Busy" etc.) You can do that in awakeFromInsert method, for example.

Then use @"sectionOrder" as both sectionNameKeyPath and the keypath in sort descriptor. You can set section titles to be "Push", "Busy" etc. using this UITableViewDataSource method: